Comparison of two regression lines over a finite interval

Area of Science:

• Statistics
• Regression Analysis

Background:

• Comparing two regression lines is crucial in various scientific fields.
• Existing methods may lack power for ordered alternatives or specific interval comparisons.

Purpose of the Study:

• To develop and present a likelihood ratio test (LRT) for comparing two regression lines.
• To test the ordered alternative hypothesis that Line 1 lies above Line 2 over a finite interval.
• To provide critical values and evaluate the power of the proposed test.

Main Methods:

• The study assumes homoscedastic normal errors for the regression models.
• A likelihood ratio test is formulated for the specified ordered alternative.
• Exact critical values are computed for common significance levels (alpha = .01, .05, .10).

Main Results:

• The likelihood ratio test provides a method for detecting when one regression line is significantly above another on a defined interval.
• A table of exact critical values is provided for practical application across different degrees of freedom.
• Power comparisons indicate the performance of the LRT against competing statistical tests.

Conclusions:

• The developed likelihood ratio test is a valuable tool for ordered regression line comparisons over finite intervals.
• The provided critical values facilitate the application of the test in empirical research.
• The LRT demonstrates competitive power, offering an effective alternative for specific hypothesis testing scenarios.